Abstract: A method is provided for solving a given combinatorial problem includes providing a function that has been established for a family of combinatorial problems including the given combinatorial problem. For each problem in the family, the function relates a secondary measure of the problem to a quality metric of a characteristic solution to the problem. The function may be applied to a value of the secondary measure for the given problem to obtain a value of the quality metric of the characteristic solution to the given problem. The given problem may be solved to obtain a solution to the given problem; and the solution evaluated based on comparison of a value of the quality metric of the solution, and the value of the quality metric of the characteristic solution. And in at least one instance based on the evaluation, the solution may be communicated to guide performance of a task.

Abstract: A method is provided for solving a given combinatorial problem includes providing a function that has been established for a family of combinatorial problems including the given combinatorial problem. For each problem in the family, the function relates a secondary measure of the problem to a quality metric of a characteristic solution to the problem. The function may be applied to a value of the secondary measure for the given problem to obtain a value of the quality metric of the characteristic solution to the given problem. The given problem may be solved to obtain a solution to the given problem; and the solution evaluated based on comparison of a value of the quality metric of the solution, and the value of the quality metric of the characteristic solution. And in at least one instance based on the evaluation, the solution may be communicated to guide performance of a task.

Abstract: Methods of benchmarking the problem solution space of a trial scenario for a combinatorial solver, as well as the characteristic performance of a combinatorial solver operating upon the trial scenario. Given a set of predetermined trial scenario data, the generalized method includes the steps of: (a) obtaining a random sequence; (b) reordering the predetermined trial scenario data into a randomized input form according to the random sequence; (c) inputting the randomized input form into a combinatorial solver; (d) solving the randomized input form with the combinatorial solver to produce a solution; (e) evaluating the solution to measure the value of a criterion of solution quality; and (f) recording the measured value of the criterion of solution quality in a data storage structure. The steps are repeated for a predetermined number of trials, whereupon the statistical distribution of the measured values is analyzed in order to determine at least one parameter of a statistical distribution function.

Abstract: A schedule optimizing algorithm improves scheduling quality, reducing a schedules cycle time and requiring only marginal increase in computer execution time. Lower quality computerized scheduling programs are substantially improved through the additional steps of sequential left time shifting and right time shifting of respective chronologically sorted completion time and starting time task listings.